Thermal Characterization and Effect of Deposited $$\hbox {CO}_{2}$$ on a Cryogenic Insulation System Based on a Spherical Powder

The objective of this work is to study the effect of deposited \(\hbox {CO}_{2}\) on the solid thermal conductivity of a cryogenic insulation system. Therefore, measurements were performed using a guarded hot plate apparatus at temperatures in the range from 80 K to 290 K in combination with a bellow acting as the sample containment. The unique experimental setup and sample preparation are described in detail. Furthermore, existing thermal models which are based on a superposition of thermal transfer due to radiation and solid thermal conductivity were modified to account for the thermal effects of deposited gases and the consequently increased solid thermal conductivity for a spherical powder. Measurements showed a significant increase of the solid thermal conductivity depending on the amount of \(\hbox {CO}_{2}\) that was provided for deposition–evacuation. 2.77 Vol-‰\(\hbox {CO}_{2}\) resulted in an increase of 5.5 % in the overall solid thermal conductivity. Twice this amount (5.54 Vol-‰\(\hbox {CO}_{2}\)) and four times this amount (11.1 Vol-‰\(\hbox {CO}_{2}\)) resulted in an increase of \(8.8\,\%\) and 14.1 % in the overall solid thermal conductivity, respectively. Due to additional temperature sensors, it was possible to measure the effective thermal conductivity in different layers of the insulation material. Thus, a significant change in the innermost layer of \(75\,\%\) was measured for the solid thermal conductivity comparing the evacuated sample with the \(\hbox {CO}_{2}\)-loaded (11.1 Vol-‰\(\hbox { CO}_{2})\) sample.     

Determination of the effective thermal conductivity of a plate in nonsteady experiment

The article describes a method of finding the effective thermal conductivity of multilayered structures at the nonsteady stage of the experiment and an experimental installation with automatic systems for setting the experimental regime and processing the experimental data.Notation thickness of the layer of heat insulation - x coordinate - t(x, ) temperature at the point of the material with the coordinate x at the instant - thermal conductivity - _ef effective thermal conductivity - c heat capacity - density of the material - C_d heat capacity of the disk per unit area of the base - m cooling rate of the disk - P_c thermal contact resistance - P_r thermal resistance of the investigated layer Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 616–620, October, 1988.     

Application of the Transient Hot-Wire Technique to the Measurement of the Thermal Conductivity of Solids

A novel application of the transient hot-wire technique for thermal conductivity measurements is described. The new application is intended to provide an accurate means of implementation of the method to the determination of the thermal conductivity of solids exemplified by a standard reference ceramic material. The methodology makes use of a soft-solid material between the hot wires of the technique and the solid of interest. Measurements of the transient temperature rise of the wires in response to an electrical heating step in the wires over a period of 20 s to 10 s allows an absolute determination of the thermal conductivity of the solid. The method is based on a full theoretical model with equations solved by finite-element method applied to the exact geometry. The uncertainty achieved for the thermal conductivity is better than ±1%, and for the product (C _p) about ±3%. The whole measurement involves a temperature rise less than 4 K.     

The influence of residual gas pressure on the thermal conductivity of microsphere insulations

Experimental results of investigations of the heat exchange by residual gas in microsphere insulations are presented. The results of measurements of microsphere effective thermal conductivity versus residual gas (N₂) pressure in the pressure range of 10^–3–10⁵ Pa are also given. A sample of self-pumping microsphere insulation was prepared and its thermal parameters were tested. In comparison to the standard microsphere insulation, the self-pumping insulation yielded lower thermal conductivity results over the entire pressure range. The stability of its thermal parameters as a result of considerable gas input into the insulation volume is discussed. Measurements of temperature and pressure distributions inside the microsphere layer were performed. Plots of temperature and pressure gradients inside the layer of the microsphere insulation are presented.Nomenclature d _m Mean value of the microsphere diameter - k Apparent thermal conductivity coefficient - ¯k Average thermal conductivity coefficient - k _c Component of the heat transfer by conduction - k _g Modified gas thermal conductivity under atmospheric pressure - k _r Component of the heat transfer by radiation - k _s Thermal conductivity of the sphere material - k _gc Component of the heat conduction by gas - k _go Gas thermal conductivity under atmospheric pressure - k _gr Sphere effective conductivity - k _ss Component of the heat conduction by the solid state - K 1–(k _g/k _gr) - Kn Knudsen number - ¯L Mean free path of gas molecules - m 1–_s; porosity - m Empty volume of a single sphere - p Residual gas pressure - ¯p Average pressure - p _g Pressure measured by gauge - p ₀ Residual gas pressure above the insulation bed - r Radial coordinate - T Temperature - T _c Temperature of the cold calorimeter wall - T _g Temperature of the pressure gauge - T _H Temperature of the hot calorimeter wall - T _i Gas temperature inside the bed - T _y Constant dependent on the sort of gas - v Volume - Accommodation coefficient - Density - _a Local distance between surfaces - _s Solid fraction - Constant dependent on the sort of gas - Time measured from the initiation of insulation cooling     

Thermophysical parameters for the combustion products from tetrazole-sodium tetrazolate mixtures

Measurements have been made on the thermal conductivity and specific heat of the powder product from quenching in nitrogen applied to the gas-liquid flame formed by the combustion of a tetrazole-sodium tetrazolate mixture in weight proportion 31. The thermal conductivity on the whole is a nonmonotone function of temperature in the range 100–450 K and has some local turning points associated with the multicomponent structure and the phase transitions associated with chemical and structural transformations.Translated from Inzhenrno-fizicheskii Zhurnal, Vol. 61, No. 3, pp. 422–426, September, 1991.     

Investigation of thermal conductivity of liquid freons

The temperature dependence of the thermal conductivity of five liquid freons is experimentally investigated. An empirical relation for generalization of the obtained data is offered. The thermal conductivity of liquid Freons 11, 21, 114, and 115 is calculated.Notations thermal conductivity - C_c and C₀ total heat capacities of inner cylinder and layer of test liquid - D₂ and D₁ outside diameter of layer and inner cylinder, respectively - m cooling rate; M-correction for system heat loss - B constant coefficient for given liquid - n exponent - A molecular constant of liquid - a_r atomic constant - x, y, z, q number of atoms of carbon, fluorine, chlorine, and hydrogen in the freon molecule - density of liquid - molecular mass     

Basic Problems in Thermal-Conductivity Measurements of Soils

The thermal conductivity of pozzolanic soil (a fine sandy, unconsolidated, alluvial soil from Lazio, Italy, based on volcanic ash) and blue marlstone rocks (from Alba, Piedmont, north Italy) was measured, using a thermal probe technique, over a wide range of temperatures from ${-}20\,^\circ \mathrm{C}$ to ${+}20\,^\circ \mathrm{C}$ . Unfrozen pozzolanic soil thermal-conductivity data display surprisingly low values about 3 to 4 times smaller than water; for frozen soils, the data are just slightly higher than for the unfrozen state but they are still 2 to 3 times lower than for water and seven times lower than for ice. This outcome is probably due to a high internal porosity of individual volcanic ash particles. The influence of the bulk soil porosity on the measured thermal conductivity was found to be rather negligible; the observed slight variation of the thermal conductivity is possibly due to the diverse grain size distribution of soil samples excavated from different depths of the ground. The blue marlstone rock has a considerably higher thermal conductivity than pozzolanic soil, likely due to its very small porosity, consolidated structure, and different implicated minerals. The frozen rock has just about a 30 % higher thermal conductivity than that for the unfrozen state. A temperature-dependent thermal conductivity is observed in the freezing state only. Test results show how heat transfer between the thermal probe and surrounding soil is influenced by storage of heat in the tested material, conduction heat flow, water evaporation due to heating, and finally by vapor diffusion and circulation.     

Determination of the thermal conductivity of polypyrrole over the temperature range 280–335 K

Samples of polypyrrole were synthesised under galvanostatic conditions to produce films possessing a range of electrical conductivity from 10^–3 to 10 S cm^–1. The electrical and thermal conductivity of these films has been determined between 280 and 335 K. The electrical conductivity was measured using a four probe technique calibrated against ASTM D4496-87. Thermal conductivity was determined from measurements of thermal diffusivity, specific heat and density. Thermal diffusivity was determined using a modified a.c. calorimetry technique, while differential scanning calorimetry (DSC) was used to determine specific heat. The polymer's density was measured using Archimedes' principle. The results were used to calculate the Lorenz number of polypyrrole. A comparison of the predicted behaviour and experimental results was made. Thermal conductivity is found to be large compared to that predicted from the electrical conductivity measurements on low conductivity films. Molecular vibration effects are found to be non-trivial and experimental means for measuring their contribution are mentioned. While polypyrrole has been regarded as a synthetic metal the thermal conductivity results show this classification is wrong.     

Thermal Relaxation of 3He Solid Films Adsorbed on Graphite

No Heading The thermal conductivity between the ³He solid films and the graphite substrate was measured by the relaxation method between 100 K and 1 mK. The areal-density depedence of the thermal conductivity shows behavior similar to that of the exchange frequency J both in the submonolayer and in the second layer. These facts indicate that heat is transferred by magnetic mechanisms in the ³He solid film itself. They also imply that the ³He solid film is thermally connected with the graphite substrate only at some local spots.PACS numbers: 67.70.+n, 67.80.Gb     

Novel materials for thermal via incorporation into SOI structures

Self-heating effects in ICs on silicon-on-insulator (SOI) substrates are due to the thick buried oxide layer present in the SOI substrate. Silicon dioxide has a poor thermal conductivity value (0.4-1.2WK^-1m^-1), compared with silicon (150WK^-1m^-1). In order to minimize this self-heating, the use of multiple-layer structures as thermal vias (TV) is investigated. The vias have been fabricated as sandwich layers with thin SiO₂ (20 nm) enclosing low pressure chemical vapor deposited (LPCVD) silicon layers (1 m), all IC compatible materials. The LPCVD silicon layers consisted of either polycrystalline silicon or a combination of amorphous silicon and polysilicon. Electrical testing of the oxide/silicon structures has shown that inclusion of an amorphous silicon layer in the oxide sandwich improves the interface between the oxide and the silicon layer. This provides better electrical stability with an operational capability >30 V. The capacitance of the multi-layer structure (96 pF), as measured at frequencies 1 MHz, confirms that the polysilicon behaves as a dielectric layer at these frequencies. Thermal conductivity assessment, using a four-terminal resistor structure, shows that the multilayer via offers an improved thermal conductivity (3.5WK^-1m^-10 when compared to a 1-m homogenous buried oxide layer (0.8WK^-1m^-1)     

Phase behavior and thermal conductivity of urea at pressures up to 1 GPa and at temperatures in the range 50–370 K

The thermal conductivity of the solid phases I and III of urea was measured at temperatures in the range 50–370 K for pressures up to 1 GPa. Phase III, previously detected only at pressures above 0.5 GPa, was observed here at low pressures ( <0.07 GPa) below about 230 K. Extrapolation of the I–III phase line indicates that phase III might be obtained at 218 K at atmospheric pressure and, consequently, that urea might exhibit two solid phases at atmospheric pressure. The temperature dependence of the thermal conductivity of both phase I and phase III could be described by the Debye model for thermal conductivity assuming phonon scattering by three phonon umklapp processes only. Despite a volume decrease at the I III transition, the thermal conductivity decreased by about 20%. Normally, thermal conductivity increases at a phase transition at which volume decreases. This rather unusual behavior of urea might be due to an increase in the nearest-neighbor distance at the I III transition.     

Thermal conductivity of dense and porous yttria-stabilized zirconia

The thermal conductivity of dense and porous yttria-stabilized zirconia (YSZ) ceramics has been measured as a function of temperature in the range 25 to 1000 °C. The dense specimens were either single crystal (8 mol% YSZ) or sintered polycrystalline (3 mol% and 8 mol% YSZ). The porous specimens (3 mol% YSZ) were prepared using the fugitive polymer method, where different amounts of polymer spheres (of two different average sizes) were included in the starting powders before sintering. This method yielded materials with uniformly distributed porosities with a tight pore-size distributions. A theory has been developed to describe the thermal conductivity of dense YSZ as a function of temperature. This theory considers the reduction in the intrinsic thermal conductivity due scattering of phonons by point defects (oxygen vacancies and solute) and by the hopping of oxygen vacancies. It also considers an increase in the effective thermal conductivity at high temperatures due to radiation. This theory captures the essential features of the observed thermal conductivity. The Maxwell theory has been used to analyze the thermal conductivity of the porous materials. An adequate agreement was found between the theory and experiment.     

Thermal conduction mechanism of aluminium nitride ceramics

Extremely large grain size AIN ceramics were produced by HIP sintering at an ultra-high temperature of 2773 K without reducing the oxygen content in order to determine experimentally whether the factor controlling thermal conductivity is either grain boundaries or the internal structure of the grains. The room-temperature thermal conductivity of the HIPed AIN with a grain size of 40 m was 155 Wm^–1 K^–1, and was almost equal to that of the normally sintered AIN with a grain size of 4 m. Therefore, thermal conductivity at room temperature is independent of AIN grain size, or the number and amount of grain-boundary phase for reasonably well-sintered AIN ceramics. The calculated phonon mean free path of sintered bodies was 10–30 nm at room temperature, which is too small to compare with the AIN grain size. Consequently, it is shown that the thermal conductivity of sintered AIN is controlled by the internal structure of the grains, such as oxygen solute atoms.     

Measurements of Thermal Conductivity and Thermal Diffusivity of CVD Diamond

The thermal conductivity of natural, gem-quality diamond, which can be as high as 2500 Wm^–1 K^–1 at 25°C, is the highest of any known material. Synthetic diamond grown by chemical vapor deposition (CVD) of films up to 1 mm thick exhibits generally lower values of but under optimal growth conditions it can rival gem-quality diamond with values up to 2200 Wm^–1 K^–1. However, it is polycrystalline and exhibits a columnar microstructure. Measurements on free-standing CVD diamond, with a thickness in the range 25–400 m, reveal a strong gradient in thermal conductivity as a function of position z from the substrate surface as well as a pronounced anisotropy with respect to z. The temperature dependence of in the range 4 to 400 K has been analyzed to determine the types and numbers of phonon scattering centers as a function of z. The defect structure, and therefore the thermal conductivity, are both correlated with the microstructure. Because of the high conductivity of diamond, these samples are thermally thin. For example, laser flash data for a 25-m-thick diamond sample is expected to be virtually the same as laser flash data for a 1-m-thick fused silica sample. Several of the techniques described here for diamond are therefore applicable to much thinner samples of more ordinary material.     

Thermal-Conductivity Measurements of Aqueous Orthophosphoric Acid Solutions in the Temperature Range from (293 to 400) K and at Pressures up to 15 MPa

A new improved guarded parallel-plate thermal-conductivity cell for absolute measurements of corrosive (chemically aggressive) fluids under pressure has been developed. Using the new modified guarded parallel-plate apparatus the thermal conductivity of aqueous orthophosphoric acid solutions was measured over the temperature range from (293 to 400) K and pressures up to 15 MPa. Measurements were made for three compositions of \(\text {H}_{3}\text {PO}_{4}\) (8 mass%, 15 mass%, and 50 mass%) along three isobars of (0.101, 5, and 15) MPa. The combined expanded uncertainty of the thermal-conductivity \((\lambda )\) measurements at the 95 % confidence level with a coverage factor of \(k=2\) is estimated to be 2 %. The uncertainties of the temperature, pressure, and concentration measurements were 15 mK, 0.05 %, and 0.01 %, respectively. The temperature, concentration, and pressure dependences of the thermal conductivity of the solution were studied. The measured values of thermal conductivity were compared with the available reported data and the values calculated from various correlation and prediction models. A new wide-range correlation model (extended Jones–Dole type equation with pressure-dependent coefficients) for the \(\text {H}_{3}\text {PO}_{4}\) (aq) solution was developed using the present experimental data.     

Heat transfer from a cylindrical heater to solidified refrigerants

The results of an experimental investigation of the equivalent thermal conductivity of the gas layer forming around a cylindrical heater placed in a solidified gas (argon or nitrogen) at pressures P 3 mm Hg are given for thermal fluxes of up to 50 W/m².Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 4, pp. 669–674, October, 1975.     

The thermal conductivity of benzene and toluene

The thermal conductivity of liquid toluene and benzene was measured in the temperature range 298 to 370 K, near the saturation line, using an absolute transient hot-wire technique. The measurements were made in a modified version of an existing instrument, equipped with a new automatic Wheatstone bridge, computer controlled. The bridge measures the time that the resistance of a 7-m-diameter platinum wire takes to reach predetermined values, programmed by the computer. The computer can generate up to 1024 analog voltages, via a 12-bit D/A converter. The accuracy of the measurements with this new arrangement was assessed by measuring the thermal conductivity of a primary standard, toluene, at several temperatures and was found to be of the order of 0.3%. Benzene was chosen because it is under study as a possible secondary standard for liquid thermal conductivity by the Subcommittee on Transport Properties of IUPAC.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Quantitative Thermal Microscopy Measurement with Thermal Probe Driven by dc+ac Current

Quantitative thermal measurements with spatial resolution allowing the examination of objects of submicron dimensions are still a challenging task. The quantity of methods providing spatial resolution better than 100 nm is very limited. One of them is scanning thermal microscopy (SThM). This method is a variant of atomic force microscopy which uses a probe equipped with a temperature sensor near the apex. Depending on the sensor current, either the temperature or the thermal conductivity distribution at the sample surface can be measured. However, like all microscopy methods, the SThM gives only qualitative information. Quantitative measuring methods using SThM equipment are still under development. In this paper, a method based on simultaneous registration of the static and the dynamic electrical resistances of the probe driven by the sum of dc and ac currents, and examples of its applications are described. Special attention is paid to the investigation of thin films deposited on thick substrates. The influence of substrate thermal properties on the measured signal and its dependence on thin film thermal conductivity and film thickness are analyzed. It is shown that in the case where layer thicknesses are comparable or smaller than the probe–sample contact diameter, a correction procedure is required to obtain actual thermal conductivity of the layer. Experimental results obtained for thin SiO\(_{\mathrm {2}}\) and BaTiO\(_{\mathrm {3 }}\)layers with thicknesses in the range from 11 nm to 100 nm are correctly confirmed with this approach.     

Stability of the interphase surface in the freezing of moist ground

It is suggested that the formation of ice layers should be regarded as a consequence of a loss of stability of the motion of the freezing front. The kinetics of the freezing process is investigated and a stability criterion is obtained.Notation s(t) coordinate of the moving front - L length of the specimen - k moisture conductivity - W moisture content - heat of phase transition - W_H amount of unfrozen water - q flow of moisture from the melted zone into the frozen zone - v velocity of motion of the front - T_i temperature - Q_i heat flux - _i thermal conductivity - a_i thermal diffusivity (i=1 is the frozen zone and i=2 is the melted zone) - mass transfer coefficient - T_H the initial temperature Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 96–101, July, 1980.     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure